The invention pertains to a mechanism for moving a length of web material, more particularly to a mechanism developed to move a piece of cloth from one position to another, accurately and with a controlled motion that can be related to other operations being performed on the cloth. In the garment industry, it is necessary to have a mechanical device which will remain at rest until a piece of cloth is in a position to be moved. Upon receipt of the control signal indicating this condition, the mechanism must grip the cloth and move it a predetermined distance where it is to be released to fall in a stack. If successive pieces of cloth are moved and released a stack will be formed at the release point. It is necessary that each piece of cloth be located accurately with respect to the piece before it. The location of the gripping, the location of the release, the distance to be moved, and the rate of movement must be variables that can be preset into the mechanism. Commercial "stackers" for the garment industry to carry out these functions will only perform some but not all of them. Furthermore, such prior art stackers are inaccurate, unreliable, difficult to control, and require too much space.